A forced two-horizontal-dimension analytical model is developed to investigate the distinguishing physical features of landslide-induced tsunamis generated and propagating on a plane beach. The analytical solution is employed to study the wave field at small times after the landslide motion starts. At larger times, the occurrence of transient edge waves travelling along the shoreline is demonstrated, showing the differences with the transient waves propagating over a bottom of constant depth. Results are satisfactorily compared with available experimental data. Finally, the validity of non-forced numerical models is discussed

We present a depth-integrated equation for the mechanics of propagation of lowfrequency\ud hydroacoustic waves due to a sudden bottom displacement associated with\ud earthquakes. The model equation can be used for numerical prediction in large-scale\ud domains, overcoming the computational difficulties of three-dimensional models and so\ud creating a solid base for tsunami early warning systems

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For flood protection against storm tides, barriers of box-like gates hinged along a bottom axis have been designed to span the three inlets of the Venice Lagoon. While on calm days the gates are ballasted to rest horizontally on the seabed, in stormy weather they are raised by buoyancy to act as a dam which is expected to swing to and fro in unison in response to the normally incident sea waves. Previous laboratory experiments with sinusoidal waves have revealed however that neighbouring gates oscillate out of phase, at one half the wave frequency, in a variety of ways, and hence would reduce the effectiveness of the barrier. Extending the linear theory of trapped waves by Mei et al. (1994), we present here a nonlinear theory for subharmonic resonance of mobile gates allowed to oscillate about a vertical plane of symmetry. In this part (1) the evolution equation of the Landau–Stuart type is first derived for the gate amplitude. The effects of gate geometries on the coefficients in the equation are examined. After accounting for dissipation effects semi-empirically the theoretical results on the equilibrium amplitude excited by uniform incident waves are compared with laboratory experiments.

Abstract. This work proposes an advancement in analytical modelling of landslide tsunamis propagating along a plane beach. It is divided into two parts. In the first one, the analytical two-horizontal-dimension model of Sammarco and Renzi (2008) for tsunamis generated by a Gaussian-shaped landslide on a plane beach is revised and extended to realistic landslide shapes. The influence of finiteness and shape of the slide on the propagating waves is investigated and discussed. In the second part, a new model of landslide tsunamis propagating along a semi-plane beach is devised to analyse the role of the continental platform in attenuating the wave amplitude along the shoreline. With these parameters taken into account, the fit with available experimental data is enhanced and the model completed.

We consider a flap-gate farm, i.e. a series of P arrays, each made by Q neighboring flap gates, in an infinitely long channel. We show that there are P × ( Q − 1) natural modes and determine their eigenfrequencies and modal forms. When the distance between the arrays goes to infinity the eigenfrequencies converge to the Q − 1 values given by Li and Mei [ 14 ]. For an ad-hoc combination of channel geometry and flap gate characteristics, modal excitation can give significantly larger response than for the case of a single or a sparse gate system. This aspect is relevant for the design of an optimal gate farm wave energy converter.

An analytical forced two-horizontal-dimension model is derived to investigate landslide tsunamis propagating around a conical island lying on a flat continental platform. Separation of variables and Laplace transform are used to obtain the free-surface elevation in the whole domain and the runup at the shoreline in terms of confluent Heun functions. The main properties of these functions and their asymptotic behaviour for large parameters are investigated. Expression of the transient leading wave travelling offshore is also derived. The distinguishing physical features of landslide tsunamis propagating in a round geometry are then pointed out and compared with those of landslide tsunamis propagating along a straight coast. Analytical results satisfactorily agree with available experimental data.

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